Transit visum after 2.5 week in China

Hi,
I am planning to go to China in May. I arrive in Beijing (PEK) from Amsterdam (AMS) and will travel for 2.5 weeks in China on a tourism L type. Afterwards we go to Hong Kong and Taiwan and after 1.5 week we fly from Taipei (TPE) to Beijing (PEK) to go back to Amsterdam (AMS) again within 72 hours. Is it possible to apply for a transit visa the second time? Or do we need a double-entry visa?

The flight from TPE > PEK and PEK > AMS is on the same airport and within 3 hours.
Greetings,
Thomas